ModularTrace

The trace of a matrix in $\mathrm{PSL}(2,\mathbb{Z})$.

ModularTrace(matrix)$a+d$

Typed signatures

Type	Package	Applies
(expression<ModularMatrix> | list | string) -> integer	modular	always

Domain: The modular group

Examples

Basic #

$1+2$

live ↗

In$\mathrm{ModularTrace}(\mathrm{ModularMatrix}(1, 1, 1, 2))$Out$3$

About

Examples	1

Implementation

mappedwolframpackages/oracle/src/mappings.ts

A plain matrix's trace is Wolfram's own Tr[{{a,b},{c,d}}], but this head also accepts an LR word directly and a chain of ModularMatrix/ModularSTWord calls -- the same word/matrix duality ModularMatrix's own entry notes Wolfram has no heads for, so the whole head is left unmapped rather than covering only the plain-matrix call shape. Wolfram Function Repository searched (modular group / PSL2Z / trace); only ModularTessellation turned up, an unrelated upper-half-plane drawing tool.

See also: ModularKind, ModularMatrix